Author: alexyoucis

Punctured disks and punctured curves and cohomology, oh my! (Part I: the proper curve case)

This is the first in a series of posts whose goal is to compute the cohomology of the (several times) punctured closed p-adic disk \mathbb{B}_{\mathbb{C}_p}-\{p_1,\ldots,p_m\} as well as the cohomology of smooth (and some non-smooth) algebraic curves.

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A smattering of representation theory

Attached below are notes that I wrote for a seminar at Berkeley.

The goal of the notes was to understand some of the representation theory surrounding Scholze’s paper on the cohomology of the Lubin–Tate tower. In particular I, Koji Shimizu, DongGyu Lim, and Sander Mack-Crane were/are interested in understanding whether there is a function field analogue of this paper.

In particular, it has an eye towards modular (i.e. mod p) representations of p-adic groups. So, it discusses some of the classical theory of representations of p-adic groups from a categorical perspective which serves one better in the modular representation setting. It also discusses the fascinating theorem of Kazhdan relating Hecke algebras for G(F) and G(F') where F and F'are soemthing like the tilts of F and F'.

Enjoy!

Modular reps